Maxwell's equations for the electric field \(\mathbf{E}\) and magnetic field \(\mathbf{B}\) are

where \(ho\) is the charge density, \(\mathbf{J}\) is the current density, and \(\epsilon_{0}\) and \(\mu_{0}\) are (respectively) the permittivity and permeability of the vacuum, both constants. Derive the vacuum wave equations for \(\mathbf{E}\) and for \(\mathbf{B}\). Hint: You can use the vector identity \(abla \times(abla \times \mathbf{A})=\) \(abla(abla \cdot \mathbf{A})-abla^{2} \mathbf{A}\) where \(\mathbf{A}\) is any vector.

Transcribed Image Text:

VE 4p, V.B=0, VxE 1 OB = - Vx B = 4 C 1 2 J+